What is the Greatest Common Factor of 82144 and 82164?

Greatest common factor (GCF) of 82144 and 82164 is 4.

GCF(82144,82164) = 4

We will now calculate the prime factors of 82144 and 82164, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82144 and 82164.

How to find the GCF of 82144 and 82164?

We will first find the prime factorization of 82144 and 82164. After we will calculate the factors of 82144 and 82164 and find the biggest common factor number .

Step-1: Prime Factorization of 82144

Prime factors of 82144 are 2, 17, 151. Prime factorization of 82144 in exponential form is:

82144 = 2⁵ × 17¹ × 151¹

Step-2: Prime Factorization of 82164

Prime factors of 82164 are 2, 3, 41, 167. Prime factorization of 82164 in exponential form is:

82164 = 2² × 3¹ × 41¹ × 167¹

Step-3: Factors of 82144

List of positive integer factors of 82144 that divides 82144 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 151, 272, 302, 544, 604, 1208, 2416, 2567, 4832, 5134, 10268, 20536, 41072

Step-4: Factors of 82164

List of positive integer factors of 82164 that divides 82144 without a remainder.

1, 2, 3, 4, 6, 12, 41, 82, 123, 164, 167, 246, 334, 492, 501, 668, 1002, 2004, 6847, 13694, 20541, 27388, 41082

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82144 and 82164. The biggest common factor number is the GCF number.
So the greatest common factor 82144 and 82164 is 4.

Also check out the Least Common Multiple of 82144 and 82164